On the combined effects of surface tension force calculation and interface advection on spurious currents within Volume of Fluid and Level Set frameworks

This paper deals with the comparison of Eulerian methods to take into account the capillary contribution in the vicinity of a fluid–fluid interface. Eulerian methods are well- known to produce additional vorticity close to the interface that leads to non-physical spurious currents. Numerical equilibrium between pressure gradient and capillary force for the static bubble test case within a VOF framework has been reached in [35] with the height-function technique [14,35]. However, once the bubble is translated in a uniform flow, spurious currents are maintained by slight errors induced by translation schemes. In this work, two main points are investigated: the ability of Volume of Fluid and Level Set methods to accurately calculate the curvature, and the magnitude of spurious currents due to errors in the calculation of the curvature after advection in both translating and rotating flows. The spurious currents source term is expressed from the vorticity equation and used to discuss and compare the methods. Simulations of gas–liquid Taylor flow at low capillary number show that the flow structure and the bubble velocity can be significantly affected by spurious currents

Artificial viscosity model to mitigate numerical artefacts at fluid interfaces with surface tension

The numerical onset of parasitic and spurious artefacts in the vicinity of uid interfaces with surface tension is an important and well-recognised problem with respect to the accuracy and numerical stability of interfacial ow simulations. Issues of particular interest are spurious capillary waves, which are spatially underresolved by the computational mesh yet impose very restrictive time-step requirements, as well as parasitic currents, typically the result of a numerically unbalanced curvature evaluation. We present an arti cial viscosity model to mitigate numerical artefacts at surface-tension-dominated interfaces without adversely a ecting the accuracy of the physical solution. The proposed methodology computes an additional interfacial shear stress term, including an interface viscosity, based on the local ow data and uid properties that reduces the impact of numerical artefacts and dissipates underresolved small scale interface movements. Furthermore, the presented methodology can be readily applied to model surface shear viscosity, for instance to simulate the dissipative e ect of surface-active substances adsorbed at the interface. The presented analysis of numerical test cases demonstrates the e cacy of the proposed methodology in diminishing the adverse impact of parasitic and spurious interfacial artefacts on the convergence and stability of the numerical solution algorithm as well as on the overall accuracy of the simulation results

Simulation of micro-flow dynamics at low capillary numbers using adaptive interface compression

A numerical framework for modelling micro-scale multiphase flows with sharp interfaces has been developed. The suggested methodology is targeting the efficient and yet rigorous simulation of complex interface motion at capillary dominated flows (low capillary number). Such flows are encountered in various configurations ranging from micro-devices to naturally occurring porous media. The methodology uses as a basis the Volume-of-Fluid (VoF) method combined with additional sharpening smoothing and filtering algorithms for the interface capturing. These algorithms help the minimisation of the parasitic currents present in flow simulations, when viscous forces and surface tension dominate inertial forces, like in porous media. The framework is implemented within a finite volume code (OpenFOAM) using a limited Multidimensional Universal Limiter with Explicit Solution (MULES) implicit formulation, which allows larger time steps at low capillary numbers to be utilised. In addition, an adaptive interface compression scheme is introduced for the first time in order to allow for a dynamic estimation of the compressive velocity only at the areas of interest and thus has the advantage of avoiding the use of a-priori defined parameters. The adaptive method is found to increase the numerical accuracy and to reduce the sensitivity of the methodology to tuning parameters. The accuracy and stability of the proposed model is verified against five different benchmark test cases. Moreover, numerical results are compared against analytical solutions as well as available experimental data, which reveal improved solutions relative to the standard VoF solver

Direct numerical simulation of multi-phase flow in complex media

Tesi en modalitat de compendi de publicacionsIn numerous applications, two-phase liquid-gas transport at sub-millimeter length scales plays a substantial role in the determination of the behavior of the system at hand. As its main application, the present work focuses on the polymer electrolyte membrane (PEM) fuel cells. Desirable performance and operational life-time of this class of high-throughput energy conversion devices requires an effective water management, which per se relies on proper prediction of the water-air transport mechanisms. Such two-phase flow involves interfacial forces and phenomena, like hysteresis, that are associated with the physicochemical properties the liquid, gas, and if present, the solid substrate. In this context, numerical modeling is a viable means to obtain valuable predictive understanding of the transport mechanisms, specially for cases that experimental analyses are complicated and/or prohibitively expensive. In this work, an efficient finite element/level-set framework is developed for three-dimensional simulation of two-phase flow. In order to achieve a robust solver for practical applications, the physical complexities are consistently included and the involved numerical issues are properly tackled; the pressure discontinuity at the liquid-gas interface is consistently captured by utilizing an enriched finite element space. The method is stabilized within the framework of variational multiscale stabilization technique. A novel treatment is further proposed for the small-cut instability problem. It is shown that the proposed model can provide accurate results minimizing the spurious currents. A robust technique is also developed in order to filter out the possible noises in the level-set field. It is shown that it is a key to prevent irregularities caused by the persistent remnant of the spurious currents. It is shown how the well-established contact-line models can be incorporated into the variational formulation. The importance of the inclusion of the sub-elemental hydrodynamics is also elaborated. The results presented in the present work rely on the combination of the linearized molecular kinetic and the hydrodynamic theories. Recalling the realistic behavior of liquids in contact with solid substrates, the contact--angle hysteresis phenomenon is taken into account by imposing a consistent pinning/unpinning mechanism developed within the framework of the level-set method. Aside from the main developments, a novel technique is also proposed to significantly improve the accuracy and minimize the the loss in the geometrical features of the interface during the level-set convection based on the back and forth error compensation correction (BFECC) algorithm. Within the context of this thesis, the numerical model is validated for various cases of gas bubble in a liquid and liquid droplets in a gas. For the latter scenario, besides free droplets, the accuracy of the proposed numerical method is assessed for capturing the dynamics droplets spreading on solid substrates. The performance of the model is then analyzed for the capturing the configuration of a water droplet on an inclined substrate in the presence the contact--angle hysteresis. The proposed method is finally employed to simulate the dynamics of a water droplet confined in a gas channel and exposed to air-flow.Existen numerosas aplicaciones industriales en las que transporte bifásico (líquido-gas) a escalas submilimétricas resulta crucial para la determinación del comportamiento del sistema en cuestión. Entre todas ellas, el presente trabajo se centra en las pilas de combustible con membrana de electrolito polimérico (PEMFC). El rendimiento deseable y la vida útil operativa de esta clase de dispositivos de conversión de energía de alto rendimiento requieren una gestión eficaz del agua (conocida como “water management”), que per se depende de la predicción adecuada de los mecanismos de transporte de agua y aire. Así pues, el análisis del flujo microfluídico de dos fases obliga considerar fuerzas y fenómenos interfaciales, tales como la histéresis, que están asociados con las propiedades fisicoquímicas del líquido, el gas y, si está presente, el sustrato sólido. En este contexto, la modelización numérica es una alternativa viable para obtener una predicción precisa de los mecanismos de transporte, especialmente en aquellos casos en los que los análisis experimentales son prohibitivos, ya sea por su complejidad o coste económico. En este trabajo, se desarrolla un marco eficiente, basado en la combinación del método de elementos finitos y el método de “level-set”, para la simulación tridimensional de flujos bifásicos. Con el fin de lograr una herramienta numérica robusta para aplicaciones prácticas, las complejidades físicas se incluyen consistentemente y los problemas numéricos involucrados se abordan adecuadamente. Concretamente, la discontinuidad de la presión en la interfaz líquido-gas se captura consistentemente utilizando un espacio de elementos finitos enriquecido. La estabilización del método se consigue mediante la introducción de la técnica de multiescalas variacionales. Asimismo, se propone también un tratamiento novedoso para el problema de la inestabilidad de tipo “small-cut”. Se muestra que el modelo propuesto puede proporcionar resultados precisos minimizando las corrientes espurias en la interfaz liquido-gas. Complementariamente, se presenta una nueva metodología para filtrar el ruido en el campo de “level-set”. Esta metodología resulta ser crucial para prevenir las irregularidades provocadas por el remanente persistente de las corrientes espurias. El comportamiento de la línea de contacto es considerado a través de la inclusión los modelos correspondientes en la formulación variacional. A este respecto, el presente trabajo aborda la importancia de la inclusión de la hidrodinámica subelemental. Los resultados presentados se basan en la combinación de la cinética molecular linealizada y las teorías hidrodinámicas. Para representación del comportamiento realista de los líquidos en contacto con sustratos sólidos, el fenómeno de histéresis del ángulo de contacto se tiene en cuenta imponiendo un mecanismo de anclado / desanclado consistente desarrollado en el marco del método de level-set. Aparte de los desarrollos principales, también se propone una técnica novedosa para la convección de la función ”level-set”. Ésta permite mejorar significativamente la precisión, minimizando a su vez la pérdida en las características geométricas de la interfaz asociadas al transporte. Esta nueva metodología está basada en el algoritmo de corrección de compensación de errores (BFECC). La herramienta numérica desarrollada en esta tesis es validada para varios casos que involucran burbujas de gas en un líquido y pequeñas gotas de líquido en un gas. Para el último escenario, además de las gotas libres, se evalúa la precisión de la herramienta propuesta para capturar la dinámica de las gotas sobre sustratos sólidos. A continuación, se analiza el rendimiento del modelo para capturar la configuración de una gota de agua sobre un sustrato inclinado en presencia de la histéresis del ángulo de contacto. El método propuesto finalmente se aplicaPostprint (published version

Experimental investigation of solubility trapping in 3D printed micromodels

Understanding interfacial mass transfer during dissolution of gas in a liquid is vital for optimising large-scale carbon capture and storage operations. While the dissolution of CO2 bubbles in reservoir brine is a crucial mechanism towards safe CO2 storage, it is a process that occurs at the pore-scale and is not yet fully understood. Direct numerical simulation (DNS) models describing this type of dissolution exist and have been validated with semi-analytical models on simple cases like a rising bubble in a liquid column. However, DNS models have not been experimentally validated for more complicated scenarios such as dissolution of trapped CO2 bubbles in pore geometries where there are few experimental datasets. In this work we present an experimental and numerical study of trapping and dissolution of CO2 bubbles in 3D printed micromodel geometries. We use 3D printing technology to generate three different geometries, a single cavity geometry, a triple cavity geometry and a multiple channel geometry. In order to investigate the repeatability of the trapping and dissolution experimental results, each geometry is printed three times and three identical experiments are performed for each geometry. The experiments are performed at low capillary number representative of flow during CO2 storage applications. DNS simulations are then performed and compared with the experimental results. Our results show experimental reproducibility and consistency in terms of CO2 trapping and the CO2 dissolution process. At such low capillary number, our numerical simulator cannot model the process accurately due to parasitic currents and the strong time step constraints associated with capillary waves. However, we show that, for the single and triple cavity geometry

Hydrodynamics of bubble column reactors in floating conditions

Les réacteurs à colonne à bulles gaz-liquide-solide sont largement utilisés liquide ainsi que gaz dans les raffineries de pétrole et les usines de traitement de gaz. Ils sont notamment utilisés dans les procédés chimiques mettant en jeu des réactions. Ces dernières années, l'industrie pétrolière et gazière offshore s'est de plus en plus intéressée à l'extension de l'application des réacteurs pour les plates formes flottantes telles que les unités flottantes de stockage et de déchargement de production (FPSO ). Cependant, les enjeux des courants marins et des vagues influencent les performances des réacteurs installés à bord des unités marines. Pour maintenir la capacité et les spécifications de produit dans de tels réacteurs, la prédiction de leurs écarts de performance par rapport à ceux statiques est essentielle. En particulier, l'étude du comportement d'un écoulement à bulle unique dans une colonne en mouvement fournira une base pour comprendre le comportement plus complexe d'un écoulement à bulles multiple s dans un réacteur à colonne à bulles fonctionnant dans des conditions flottantes. Afin de mieux comprendre les effets de la houle marine sur les performances des réacteurs à colonnes à bulles, cette recherche vise à étudier l'hydrodynamique de la remonté e d'une seule bulle dans une colonne inclinée. Comme l'interaction bulle-paroi a un impact majeur sur l'hydrodynamique du réacteur à colonne à bulles dans des conditions flottantes, les modifications de la trajectoire de la bulle, de la vitesse et du rapport d'aspect imposées par les interactions bulle-paroi sont étudiées.Gas-liquid as well as gas-liquid-solid bubble column reactors are extensively used in oil refineries and gas treatment plants. They are used especially in chemical processes involving reactions. In recent years, offshore oil and gas industry has been increasingly interested in extending application of reactors for floating platforms such as floating production storage and offloading (FPSO) units. However, the challenges of marine currents and waves influence performance of reactors installed onboard marine units. To maintain the capacity and product specifications in such reactors, prediction of their performance deviations with respect to the static ones is essential. Particularly, investigation on single bubble flow behavior in a moving column will provide a basis to understand the more complex behavior in multi-bubble flow in a bubble column reactor operating in floating conditions. To provide more detailed understanding into the effects of marine swells on the performance of bubble column reactors, this research aims at studying the hydrodynamics of single bubble rising in an inclined column. As the bubble-wall interaction has a major impact on the hydrodynamics of bubble column reactor under floating conditions, the modifications in bubble trajectory, velocity, and aspect ratio imposed by the bubble-wall interactions are studied. This master thesis consists of two chapters. The first chapter contains a general introduction on the challenges brought by the need to extend the application of hydrocarbon treating facilities onboard marine units. Important information about hydrodynamics of bubble column reactors and single bubble rising in liquid are provided. Additionally, the most important issues in selection of the solver and the simulation methods are discussed. In the second chapter, the dynamics of a single ellipsoidal air bubble rising in an inclined cylindrical vessel is experimentally investigated. At the end, a general conclusion on the work performed and recommendations for future works is presented

A Benchmark Evaluation of the isoAdvection Interface Description Method for Thermally–Driven Phase Change Simulation

A benchmark study is conducted using isoAdvection as the interface description method. In different studies for the simulation of the thermal phase change of nanofluids, the Volume of Fluid (VOF) method is a contemporary standard to locate the interface position. One of the main drawbacks of VOF is the smearing of the interface, leading to the generation of spurious flows. To solve this problem, the VOF method can be supplemented with a recently introduced geometric method called isoAdvection. We study four benchmark cases that show how isoAdvection affects the simulation results and expose its relative strengths and weaknesses in different scenarios. Comparisons are made with VOF employing the Multidimensional Universal Limiter for Explicit Solution (MULES) limiter and analytical data and experimental correlations. The impact of nanoparticles on the base fluid are considered using empirical equations from the literature. The benchmark cases are 1D and 2D boiling and condensation problems. Their results show that isoAdvection (with isoAlpha reconstruct scheme) delivers a faster solution than MULES while maintaining nearly the same accuracy and convergence rate in the majority of thermal phase change scenarios